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1.
AKA New Years Day (not to be confused with New Year's Eve)

It is called Hangover Day because..
well it's obvious

everyone has a hangover today because of excessive drinking at New Year's Eve parties.
Sober Person: Hey Lofonduh, wanna go to the mall today?

Lofonduh: Naww.. my head hurts too much.

Sober Person: But no one will come!

Lofonduh: That's because it's Hangover Day.
by Rickey Minouwagaincity December 22, 2008
 
2.
The day after New Years. You had a little to much to drink that last day of the year and now for the first dayof the new year you can celebrate with all the other hungover people, or you could sleep.
Person 1: Dude my head kills from last night.

Person 2: Another typical hangover Day.
by Sarah Is Beast December 31, 2008
 
3.
The day after new years eve.
where everyone has a hangover from breaking in the new year with alcohol.
Man 1: So what are you doing for Hang Over Day?

Man 2: Sleeping.
by Damien Johnson January 01, 2008